Search results for "Fresnel diffraction"
showing 10 items of 41 documents
Achromatic Fresnel diffraction patterns
1993
Abstract A novel method for obtaining a single, but arbitrary, achromatic Fresnel diffraction pattern of any pupil with broadband parallel illumination is presented. The optical device simply consists of an achromatic objective and an on-axis zone plate. A criterion for selecting the system parameters in order to minimize the residual chromatic aberrations is given. The recording of the selected diffraction field is obtained with low chromatic aberrations even for white-light illumination. An experimental verification is shown to illustrate this approach.
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
White-light Fourier transformer with low chromatic aberration.
1992
A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.
Paraxial waves in the far-field region
2002
Summary By investigating the changes suffered by a paraxial beam propagating in the near-field and in the far-field regions, it has been found a set of wave equations valid for points gradually closer to the near field. A relevant expression for the validity of the far-field approximation is given from the paraxial Helmholtz equation. It is pointed out that the well-known Fresnel number associated with every transverse diffraction pattern can be interpreted as a magnitude that measures the relative standard deviation of the Fraunhofer pattern and a first-order field, thus reporting on an integral expression suitable for a general case. Finally, the Rayleigh range of the optical beam is dedu…
Zero axial irradiance by annular screens with angular variation
1992
For optical alignment, it may be convenient to use a three-dimensional diffraction pattern with zero irradiance along the optical axis. This pattern is created here by using annular screens in the form of a phase daisy, a daisy flower, or a pie, with an even number of slices of an equal central angle and with every other slice with a phase retardation of 180 degrees . We recognize this form of angular variation as a particular solution of a wider set of functions that are able to produce zero axial irradiance.
Optical propagation of fractal fields. Experimental analysis in a single display
2001
An experimental device to show in a single display all the diffraction patterns generated by a 1D fractal structure is proposed. It is found that in addition to being the optimum display to see the evolution of the diffracted field through free space, some interesting features, such as continuous evaluation of self-similarity from the object to the far field, can be obtained experimentally.
Quasi-wavelength-independent broadband optical Fourier transformer
1999
The chromatic behaviour associated with diffractive optical elements is exploited herein to design a hybrid (diffractive-refractive) lens triplet showing very great wavelength-compensation capabilities for the Fraunhofer diffraction pattern of any diffracting screen under broadband point-source illumination. Within the paraxial Fresnel diffraction theory, we show that perfect compensation for the axial position of the Fourier transform of the input can be accomplished if we neglect the secondary spectrum of the refractive objective. Simultaneously, an achromatic correction for the scale of the Fraunhofer pattern is achieved. In this way, even for white light, only a low residual transversal…
All-incoherent dispersion-compensated optical correlator
2007
We report on a simple, spatially incoherent, wavelength-independent imaging system that, in contrast to the conventional case, exhibits a dispersion-compensated point-spread function. Our hybrid (diffractive-refractive) three-lens imaging configuration thus acts as an all-incoherent dispersion-compensated optical irradiance correlator. So the optical arrangement is well adapted to processing color information (both spatially and temporally incoherent) under natural illumination.
Focal-shift formula in apodized nontelecentric focusing systems
2007
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Parallel phase-shifting digital holography based on the fractional Talbot effect
2010
A method for recording on-axis single-shot digital holograms based on the self-imaging phenomenon is reported. A simple binary two-dimensional periodic amplitude is used to codify the reference beam in a Mach-Zehnder interferometer, generating a periodic three-step phase distribution with uniform irradiance over the sensor plane by fractional Talbot effect. An image sensor records only one shot of the interference between the light field scattered by the object and the codified parallel reference beam. Images of the object are digitally reconstructed from the digital hologram through the numerical evaluation of the Fresnel diffraction integral. This scheme provides an efficient way to perfo…